Spectrum sensing based on high/low sensing times

Abstract

Cognitive Radio spectrum sensing is one of the important technique to utilize the unused specturm for secondary user signal transmission without interference with the primary users of the spectrum. Spectrum prediction for the secondary users is very difficult when more number of antennas with different sensing times per demand. For that we have proposed spectrum sensing based on High or Low sensing times predictions for more signal transmissions by the secondary users. In this research paper, given an upper bound on total number of bands (or antennas), the problem of determining number of antennas with low and high sensing times (given the total sensing time as well as traffic over wideband of channels) is formulated and solved. In such formulation, the optimization criterion is chosen to be (maximization/minimization) average number of antennas. The dual problem deals with optimization (maximization/minimization) of low and high sensing times. The solution of dual problem readily follows. Hence, a bang bang time optimal spectrum sensing related results follow readily. It is shown that the variance of a Bernoulli Random variable, Z constitutes a logistic map in success probability ’P’. This fact is utilized to derive analytic results. Some analytical results related to number of antennas required are proved. Specifically it is shown through the results and observations, when the values assumed by Z are known integers, there is no value of success probability ’P’ for which expectation of Z equals the variance of Z.